2. Give another name for KL

Using the same-side interior angles theorem,

[tex]8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}[/tex]

Using vertical angles,

[tex]6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}[/tex]

Answer:

When subtracting two numbers you add the (additive inverse) of the number being subtracted.

Step-by-step explanation:

That's one of the rules of subtracting integers.

Answer:17

Step-by-step explanation:when we add the 12+5 together and will be the answer

Answer:

2. A is false

   B is false

   C is false

   D is true

Answer:

SAS or HL

Step-by-step explanation:

SAS, you have two sides and two angles  congruent on each triangle

HL, you have two hypotenuses and two right angles congruent

Answer:

1/2

Step-by-step explanation:

shaded sections = 4

total sections = 8

4/8

(4:4)/(8:4)

1/2

Answer:

The answer is 4:4.

Step-by-step explanation:

Since the three triangles are similar the length of LK will be 8 units.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

It is given that,

XW=LK=BC

∠WXY = ∠MLK=∠ABC

WY=10

XY=6

AB=6

ΔWXY ≅ MLK

XW=LK

XW=8

LK= 8 units

Thus, if the three triangles are similar the length of LK will be 8 units.

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Answer:

y = - [tex]\frac{2}{3}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

given

2x + 3y = 3 ( subtract 2x from both sides )

3y = - 2x + 3 ( divide through by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 1 ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{2}{3}[/tex] x + b  ← is the partial equation

to find b substitute (3, - 4 ) into the partial equation

- 4 = - 2 + b ⇒ b = - 4 + 2 = - 2

y = - [tex]\frac{2}{3}[/tex] x - 2 ← equation of parallel line

Answer:

Step-by-step explanation:

52 weeks in a year

Divide 52 by 2 = 26 weeks

26 weeks x 147 dollars = 3822 dollars

Thus the answer is 3822 dollars yearly

Answer:$3,528

Step-by-step explanation:

since there are 4 weeks in a month that would mean you would have to multiply 147 by two and that would = to $294.00/month so then you would have to multiply that by 12 so then that would = to $3,528.00 a year.

The equation that will represent how many grams of the compound that will remain is  C = 430(1-0.28)^5

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.The following formula can be used to calculate exponential decay:

C=a(1-r)^twhena = 430 grams

r = 28% = 0.28t = 5 hours

By substituting the values into the formula

C = 430(1-0.28)^5C = 83.20grams

Thus, after 5 hours the radioactive compound with mass 430 grams becomes 83.20 grams and the equation will be  

C = 430(1-0.28)^5

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The value of 57.17 as a mixed number is - 57 17/100.

A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction value remains constant. We can say that the simplified mixed number and the actual mixed number are fractions that are equivalent.

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the proper fraction that results in the mixed number.

In this case, -57.17 will be:

= -57 + (17/100)

= -57 17/100.

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Domain: (−∞,∞),{x|x∈R} and Range: (−∞,∞),{y|y∈R} for f(x)=0.5x

A relation is a function if it has only One y-value for each x-value.

Given,

Helene is selling cupcakes for $0.50 each.

The function f(x)=0.5x gives the total amount of money Helene makes after selling x cup cakes.

We need to find the domain and range of the function

solve the equation f(x)=0.5x to determine the values of the independent variable x and obtain the domain.

To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,∞),{y|y∈R}

Hence, Domain: (−∞,∞),{x|x∈R} and Range: (−∞,∞),{y|y∈R} for f(x)=0.5x

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The transformation which transforms y = x² to the graph of y = (x + 5)² as required in the task content is; a translation of 5 units leftwards.

It follows from the task content that the transformation responsible for the mapping y = x² to the graph of y = (x + 5)² is to be determined.

Since the pre-image graph given in the task content is; y = x².

Recall that a translation of a graph f(x) by k units leftward is represented as; f (x + k).

On this note, the given transformation of y = x² to the graph of y = (x + 5)² as required in the task content can be attributed to;

A horizontal shift of 5 units leftward.

Put simply, the required transformation is; a translation of the graph of y = x² 5 units leftwards.

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The length of arc LN of the circle is 7.40 units rounded to the nearest hundredth.

To calculate for the length of an arc of a circle, we use 2πr × (θ/360), where r is the radius and θ is the angle formed from the arc.

Thus we evaluate for the length of the arc as follows;

for π = 3.14, r = 4 and θ = 106°

2 × 3.14 × 4 × (106/360)°

25.12 × 0.2944

7.3953

Therefore, the length of the arc 7.3953 and rounded up to 7.40 to the nearest hundredth.

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Answer:

2.4938705426067307E - 8

Step-by-step explanation:

The monthly payment would be an amount of $226.67.

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

Mary takes out a loan for $6,000 at a simple interest rate of 12% to be paid back in 36 monthly installments.

The total payback = P× r/100 × T + P

Here P = $6,000 , r = 12, and T = 3 years

The total payback = 6,000 × 12/100 × 3 + 6,000

The total payback = 6,000 × 0.12 × 3 + 6,000

The total payback = $8,160

The total payback of the borrowings will be $8,160 over a three-year period. The monthly payment for this will be,

The monthly payment = Total payback / No. of payment

The monthly payment = 8,160/36

The monthly payment = $226.67

Therefore, the monthly payment would be an amount of $226.67.

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When two numbers added together result in 0, this is known as additive inverse. Using this notion, points on a number line are used to depict additive inverse.

The dotted points with the numbers 3 and -3 are the places on the number line.

To determine whether the points show an additive inverse:

Points 1 and 2 add up to 0.

3 + (-3) = (3 - 3) = 0

When two numbers added together result in 0, this is known as additive inverse.

Using this notion, points on a number line are used to depict additive inverse.

Thus, the points therefore display additive inverse.

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Answer: -787

188 is positive, negative and negative equals positive

559 is negative

the answer needs to be negative as 559 is negative so you add 559 and 188 and get 787 and add a negative sign so it's more "negative" than 188. (hard to explain in writing)

-787--188=-559

-787+188=-559

-559=-559

Answer:

u = 7

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Given: Number of roses = 8, Number of daisies =12 and number of marigolds 48.

Since we have given,

Number of roses = 8 , Number of daisies = 12 and number of marigolds = 48.

The factors of 8 = 2 * 2 * 2

The factors of 12 = 2 * 2 * 3

The factors of  48 = 2 * 2 * 2 * 2 * 3

Therefore, greatest common factor of  8, 12 and 48 is 4.

Therefore, the total number of arrangements = 4

Answer: 4

Based on the information in the table, the dollars that the total shipping cost will increase if the weight of an object increases by 1 pound is C. $1.50

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It should be noted that from the information, the table shows the total shipping costs for objects of different weights.

In this case, let the dollar amount be x.

Based on the information, this will be:

4x = 6

Divide

x = 6/4

x = 1.5

In conclusion, the correct option is C.

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(-3, -7).

[tex](1)y= 2x-1\\ \\ (2)y= 3x+2[/tex]

[tex]3x+2-2= 2x-1-2\\ \\3x=2x-3[/tex]

[tex]3x-2x=2x-3-2x\\ \\x=-3[/tex]

To see of the answer is correct, both of the equation should give the same y value for the x value of -3.

[tex](1)y= 2(-3)-1\\ \\ y=-6-1\\ \\y=-7[/tex]

[tex](2)y= 3(-3)+2\\ \\y=-9+2\\ \\y=-7[/tex]

(x, y)

(-3, -7).

The probability of the combined event that the next six days are all sunny is 1/4096

From the question, we have the following parameters that can be used in our computation:

Probability that it is sunny = 1/4

Probability that it is cloudy = 3/4

Number of days = 6

The probability for all six days, it is sunny is represented as

Probability = Probability that it is sunny^Number of days

Substitute the known values in the above equation, so, we have the following representation

Probability = (1/4)⁶

Express as decimal

Probability = (0.25)⁶

Evaluate the exponent

Probability = 1/4096

Hence, the probability is 1/4096

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Answer:

Step-by-step explanation:

d is the answer

Answer: 72 cm

Step-by-step explanation:

So since we know its length is 12 cm, that leaves us with finding the width. You could do that by adding the two length's together to get 24, then subtract that from the perimeter to get 12. The widths being added together must equal 12 and be the same, so we can divide by 2 to get 6 cm as the width. Then multiply 6 times 12 to get 72

Answer: A=72 cm²

Step-by-step explanation:

Let the width of the rectangle be x

Hence,  P=36 cm      l=12 cm

P=2(l+x)

P=2l+2x

P-2l=2x

Divide both parts of the equation by 2

Thus,

[tex]\displaystyle\\x=\frac{P-2l}{2} \\\\x=\frac{36-2(12)}{2}\\\\x=\frac{36-24}{2} \\\\x=\frac{12}{2} \\\\x=6 cm\\\\[/tex]

Area A=l*x

A=12*6

A=72 cm²

The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

The Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal:

m∠5 + m∠6 =180°.

The exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

In conclusion, the sum of all the angles formed by a triangle is equal to 180º:

m∠2 + m∠3 + m∠5 = 180°,

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Answer:

Let the number be x. "Seven less than a number" means that we need to subtract 7 from unknown number and result would be 34. . Then, x−7=34Add 7 on both sides of the equationx−7+7=34+7x=41.

Step-by-step explanation:

The grouped frequency distribution for the data is given as follows:

The relative frequency of an outcome in the context of an experiment is given by the number of outcomes assuming this value divided by the number of total outcomes.

Hence the grouped frequency distribution for the data in this problem is obtained considering the relative frequency of each outcome.

For example, we have that:

Hence the frequency for the age 41-45 is given as follows:

4/44 = 0.0909.

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